Images displayed on a video display may be digitally encoded, transmitted, and decoded. Digital encoding of video images offers many well-known advantages. For example, the effects of electromagnetic interference or noise may be reduced with digital data transmission techniques. In addition, conversion of video images into digital signals allows the video images to be processed with digital signal processing techniques, and also makes the video images compatible with other digital data processing technology.
Nevertheless, conversion of a video image into digital data creates a relatively large amount of digital data. A video image typically comprises a large number of picture elements (pixels). A pixel is the smallest resolvable spatial information element of a video display as seen by the viewer. A common display resolution is VGA which consists of 480 lines of 640 pixels each. Thus, each screen requires 307,200 pixels. In addition, color video images are comprised of three separate color pixel subdivisions at each pixel location, which results in 921,600 color pixel subdivisions for each screen. Full motion video requires the transmission of 30 screen images per second, which could require a total of 27.648 million pixels per second if each pixel is transmitted for each screen image.
Even if each pixel could be represented by a single bit of data, a 27.648 megabit data transmission rate would significantly limit the use of digital video data transmission. In practice, each pixel requires eight bits of data for MPEG compatible video. Therefore, it is necessary to compress the digital data using various techniques. Many image compression techniques have been developed.
One class of image compression techniques involves compression algorithms based on a frequency transform. In this technique, the image is generally divided into blocks of fixed size, such as 8.times.8 pixels. Each block is then transformed from the spatial domain to a frequency domain using a linear transform. The linear transform most commonly used for this operation is the discrete cosine transform (DCT). The discrete cosine transform has been developed in accordance with the moving pictures experts group (MPEG) algorithms, which are industry-standard algorithms used to coordinate digital signal processing of digitally-encoded video signals.
Known linear transform systems for decoding digitally-encoded video data, may involve a system that includes implementation of a binary algorithm as an electronic circuit, such as the discrete cosine transform and its inverse. Various algorithms and electronic circuits have been proposed for these linear transform systems. Nevertheless, these algorithms and electronic circuits suffer from various drawbacks. One such drawback is that a large number of discrete devices must be used in electronic circuits for such algorithms. Another drawback is that the processing time for systems implementing known algorithms may be excessive as the number of electronic circuit elements decreases. These problems are exacerbated for inverse discrete cosine transform (IDCT) circuits, which are typically used in applications that require circuit sizes to be minimized, such as at a set-up box that would be installed at a user's television set.